OBJECTIVE #9 Grade 11

(parabola, find up/down, vertex, axis symm, max/min)


Objective number 9 looks like this..........................

For the Parabola, state the direction of the opening, the coordinates of the vertex, the equation of the axis of symmetry, and the maximum or minimum value. Y=-(x-3)^2+3

1) Down; (3, 3); x=3, maximum at y=3
2) Down; (-3,-3); x=-3; maximum at y=-3
3) Up; (3, 3); x=3, minimum at y=3
4) Up; (-3, 3); x=-3; minimum at y=-3


FIRST STEP – Press y= on your calculator and put in the equation /formula for your parabola. Using the example above it is Y=-(x-3)^2+3

*Then Press Graph*


You should get a picture that looks like this


This picture answers the first question of direction of opening (it opens down). You can cross off any answers that say the direction of opening is up.



Step 2 - Now let’s try to find the coordinates of the vertex.
Press these buttons in this order; 2nd Trace 4 (if the parabola is going up press 3). Now move the cursor to the left side of the vertex and press Enter, go to the right side of the vertex and press Enter, now put your cursor where you think the vertex of the parabola is and press Enter.





*It should say at the bottom of screen
x=2.9999984( round off to 3)
y=3


This answers question #2, the coordinates of the vertex are x=3 (round off) and y=3
We cross off the #2 answer and are left with number 1.

Figuring question number 2 out also gives us the answers to numbers 3 and 4. We have only the correct answer left. I’m gonna try to explain the 3rd and 4th question though anyway.

Question #3 asks for the axis of symmetry (x value) it runs directly through the parabola at a 90 degree angle with the x axis, therefore the equation of axis of symmetry value doesn’t change from the x parabola quordinate. X=3



Question #4 is asking for the maximum height of the parabola, the y axis should tell you if you run a line going across from the peak of the parabola to the y axis. It is y=3